I among other people have a big psychological barrier to paying $0 for a $0 or donate game, despite the developer of said game being more than happy to make the game available for free. See e.g. https://spacey.space/@60sRefugee/113557156799767171 for an example of this thinking.

I would like to be explicitly make the game available for free by having the This file is a demo and can be downloaded for free option available for this type of game.

What you write is inconsistent.

A demo is never paid. And a demo is not the full game. That is what makes it a demo. You can't make a game available for free by calling it a demonstration of the full game - it is the full game.

Also, you cannot pay 0. Not paying isn't technically the same as paying 0. Because any payment will put the game into your library as a purchased item. "Paying 0" does not do this. Sure, colloquially it is the same. But if the game will get a minimum price later on, you cannot download it again, because you did not buy it, because you did not pay anything. 

So maybe it helps with your barrier if you see the consequences of not paying. No payment = no purchase & no ownership in library.

Maybe it also helps with your psychological barrier for your own games, if you put two files on the project and make one file be an individually priced item.

So you would have 

game.zip

and if you pay x or more you have access to

thankyou-wallpaper.jpg

x should be 2 bucks or more. 1 buck as a price is not really worth the effort with the payment processors.

And what kinda ticks me off are the actual demo versions that pose as a free game. Come on people. Either publish on Itch or don't. And if you do, you can have a demo version on your paid game. But putting out a "free game" with a pay what you want button is just not cool, if it is a demo. People that pay here, expect early access and access to the game, when it is done. Yeah, sure, you could collect supporter donations, but why not collect them by having your early access game paid with a free demo.